Saad A. Awan

First-Derivative Chromatic Symmetric Reconstruction For Proper Trees

Let $T$ be a tree. Stanley asked whether the chromatic symmetric function $X_T$ determines $T$ up to isomorphism. We approach this open problem by regarding $X_T$ as a polynomial in the power-sum symmetric functions $p_1, p_2, \dots$ and studying the invariant $\Phi_T = (\partial X_T/\partial p_1)|_{p_1 = 0}$. We prove...